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Wild binary segmentation for multiple change-point detection

Author

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  • Fryzlewicz, Piotr

Abstract

We propose a new technique, called Wild Binary Segmentation (WBS), for consistent estimation of the number and locations of multiple change-points in data. We assume that the number of change-points can increase to infinity with the sample size. Due to a certain random localisation mechanism, WBS works even for very short spacings between the change-points and/or very small jump magnitudes, unlike standard Binary Segmentation. On the other hand, despite its use of localisation, WBS does not require the choice of a window or span parameter, and does not lead to a significant increase in computational complexity. WBS is also easy to code. We propose two stopping criteria for WBS: one based on thresholding and the other based on what we term the “strengthened Schwarz Information Criterion”. We provide default recommended values of the parameters of the procedure and show that it offers very good practical performance in comparison with the state of the art. The WBS methodology is implemented in the R package wbs, available on CRAN. In addition, we provide a new proof of consistency of Binary Segmentation with improved rates of convergence, as well as a corresponding result for WBS.

Suggested Citation

  • Fryzlewicz, Piotr, 2014. "Wild binary segmentation for multiple change-point detection," LSE Research Online Documents on Economics 57146, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:57146
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    File URL: http://eprints.lse.ac.uk/57146/
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    References listed on IDEAS

    as
    1. Fryzlewicz, Piotr, 2007. "Unbalanced Haar technique for nonparametric function estimation," LSE Research Online Documents on Economics 25216, London School of Economics and Political Science, LSE Library.
    2. Fryzlewicz, Piotr, 2007. "Unbalanced Haar Technique for Nonparametric Function Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1318-1327, December.
    3. P. Fryzlewicz & S. Subba Rao, 2014. "Multiple-change-point detection for auto-regressive conditional heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(5), pages 903-924, November.
    4. Yao, Yi-Ching, 1988. "Estimating the number of change-points via Schwarz' criterion," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 181-189, February.
    5. Jushan Bai & Pierre Perron, 2003. "Computation and analysis of multiple structural change models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(1), pages 1-22.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    multiple change-points; change-point detection; binary segmentation; randomized algorithms; thresholding; Bayesian information criterion;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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